Particle physics and quantum field theory at the turn of the century: Old principles with new concepts

Abstract

The present state of quantum field theory (QFT) is analyzed from a new viewpoint whose mathematical basis is the modular theory of von Neumann algebras. Its physical consequences suggest new ways of dealing with interactions, symmetries, Hawking–Unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory. Interactions are incorporated by using the fact that the S matrix is a relative modular invariant of the interacting—relative to the incoming—net of wedge algebras. This new point of view allows many interesting comparisions with the standard quantization approach to QFT and is shown to be firmly rooted in the history of QFT. Its radical “change of paradigm” aspect becomes particularly visible in the quantum measurement problem.